Leo has a balance, and he's playing around with some weights and wooden blocks. He eventually gets the two sides to balance with 6 blocks and a 200-ounce weight on one side and 2 blocks and a 500-ounce weight on the other side.
How much does each wooden block weigh?

Let's solve this problem by setting up an equation based on the information given.

### Given:
- Side 1: 6 blocks + 200-ounce weight
- Side 2: 2 blocks + 500-ounce weight

Since the balance is in equilibrium, the total weight on both sides must be equal.

Let's assume the weight of each wooden block is \( x \) ounces.

### Setting up the equation:
The total weight on the first side is:
\[
6x + 200
\]
The total weight on the second side is:
\[
2x + 500
\]

Since the sides are balanced, we can set the equations equal to each other:
\[
6x + 200 = 2x + 500
\]

### Solving the equation:
1. Subtract \( 2x \) from both sides to get the \( x \) terms on one side:
   \[
   6x - 2x + 200 = 500
   \]
   \[
   4x + 200 = 500
   \]
2. Subtract 200 from both sides to isolate the \( 4x \) term:
   \[
   4x = 300
   \]
3. Divide by 4 to solve for \( x \):
   \[
   x = \frac{300}{4} = 75
   \]

So, each wooden block weighs **75 ounces**.

Would you like to dive deeper into any part of the solution, or do you have any questions?

---

Here are 5 related questions to explore:

1. What would happen if one block was removed from each side of the balance?
2. How would the solution change if each side also had an additional 50-ounce weight?
3. If each block weighed 80 ounces instead, what would be the new weight needed to balance the scale?
4. How would you solve this problem if one side had a different number of blocks than the other side?
5. What would the equation look like if the balance also had a 100-ounce counterweight on both sides?

**Tip:** When solving balance problems, always set up an equation that equates the total weight on both sides to find the unknown weight.

Learn how to solve a balance problem involving wooden blocks and weights. Discover the weight of each wooden block using a step-by-step equation setup. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation